The finite element method

O. C. Zienkiewicz, R. L. Taylor9780750650496, 0-7506-5049-4, 0750650559, 0750650508

In the years since the fourth edition of this seminal work was published, active research has further developed the Finite Element Method into the pre-eminent tool for the modelling of physical systems. Written by the pre-eminent professors in their fields, this new edition of the Finite Element Method maintains the comprehensive style of the earlier editions and authoritatively incorporates the latest developments of this dynamic field. Expanded to three volumes the book now covers the basis of the method and its application to advanced solid mechanics and also advanced fluid dynamics. Volume 1: The Basis is intended as a broad overview of the Finite Element Method. Aimed at undergraduates, postgraduates and professional engineers, it provides a complete introduction to the method. Volume 2 and Volume 3 of the Finite Element Method cover non-linear solid and structural mechanics and fluid dynamics respectively. Both are essential reading for postgraduate students and professional engineers working in these disciplines. New material on recovery, accuracy, error estimates and adaptivity.Increased coverage of mixed and hybrid methods including the Discontinuous Galerkin and Enhanced Strain Methods.Expanded chapter on incompressible behaviour and stabilization procedures.

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Table of contents :
Contents……Page 7
Preface……Page 15
1 Some preliminaries: the standard discrete system……Page 17
2 A direct approach to problems in elasticity……Page 34
3 Generalization of the finite element concepts. galerkin-weighted residual and variational approaches……Page 55
4 Plane stress and plane strain……Page 103
5 Axisymmetric stress analysis……Page 128
6 Three-dimensional stress analysis……Page 143
7 Steady-state field problems – heat conduction, electric and magnetic potential, fluid flow, etc…….Page 156
8 ‘Standard’ and ‘hierarchical’ element shape functions: some general families of C0 continuity……Page 180
9 Mapped elements and numerical integration – ‘infinite’ and ‘singularity’ elements……Page 216
10 The patch test, reduced integration, and non-conforming elements……Page 266
11 Mixed formulation and constraints – complete field methods……Page 292
12 Incompressible materials, mixed methods and other procedures of solution……Page 323
13 Mixed forumation and constraints – incomplete (hybrid) field methods, boundary/Trefftz methods……Page 362
14 Errors, recovery processes and error estimates……Page 381
15 Adaptive finite element refinement……Page 417
16 Point-based approximations; element-free Galerkin – and other meshless methods……Page 445
17 The time dimension – semi-discretization of field and dynamic problems and analytical solution procedures……Page 484
18 The time dimension – discrete approximation in time……Page 509
19 Couple systems……Page 558
20 Computer procedures for finite element analysis……Page 592
Appendix A Matrix algebra……Page 636
Appendix B Tensor-indicial notation in the approximation of elasticity problems……Page 642
Appendix C Basic equations of displacement analysis (chapter 2)……Page 651
Appendix D Some integration formulae for a triangle……Page 652
Appendix E Some integration formulae for a tetrahedron……Page 653
Appendix F Some vector algebra……Page 654
Appendix G Integration by parts in two or three dimensions (Green’s theorem)……Page 659
Appendix H Solutions exact at nodes……Page 661
Appendix I Matrix diagonalization or lumping……Page 664
Author index……Page 671
Subject index……Page 679